locally finite collection LocallyFinite 2002-01-22 13:08:13 2008-10-03 14:22:04 Definition locally finite locally countable collection locally countable topology \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} Let $\mathcal{C}$ be a collection of subsets of a topological space $X$. $\mathcal{C}$ is said to be \emph{locally finite} if for all $x\in X$ there is a neighbourhood $U$ of $x$ such that $U \cap A = \varnothing$ for all but finitely many $A \in \mathcal{C}$. Similarly, $\mathcal{C}$ is said to be \emph{locally countable} if for all $x\in X$ there is a neighbourhood $U$ of $x$ such that $U \cap A = \varnothing$ for all but countably many $A \in \mathcal{C}$.